beatingeffekten

Beatingeffekten, oft kallad the beating effect, is the periodic variation in the amplitude of a signal that occurs when two waves with similar but not identical frequencies are superposed. The phenomenon is common in acoustics, music, and radio engineering, where the interference between two tones produces noticeable fluctuations in loudness at a rate equal to the absolute difference between the frequencies.

Mathematically, two sine waves of equal amplitude can be expressed as s(t) = sin(2π f1 t) + sin(2π f2 t). Using a sum-to-product identity, this becomes s(t) = 2 sin(2π f_avg t) cos(π Δf t), where f_avg = (f1 + f2)/2 and Δf = f1 − f2. The factor cos(π Δf t) serves as an envelope that modulates the faster carrier at the average frequency f_avg. The audible effect is a tone near f_avg whose loudness rises and falls with a beat frequency Δf.

Perception and applications: Beats are most noticeable when Δf is small, typically from a few hertz up to a few tens of hertz. The beat phenomenon is widely used in instrument tuning and pitch comparison: listeners adjust pitches until the beats disappear, indicating f1 ≈ f2. In electronics, beating is exploited in heterodyning to mix signals and shift frequencies, as well as in measurement techniques that rely on frequency differences. Beating can also occur in optics and other wave systems where coherent waves interact, producing interference patterns in time or space.